The Higgs boson (\(\) ) discovered in 2012 at the CERN LHC [1]}, [2]}, [3]}
has thus far been found to have properties consistent with expectations from the
standard model (SM) [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
In particular, its spin-parity quantum numbers are consistent with \(J^{PC}=0^{++}\)  according to measurements performed
by the CMS [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}
and ATLAS [18]}, [19]}, [20]}, [21]}, [22]}, [23]} experiments.
It is still to be determined whether small anomalous couplings contribute to the \(\)  or \(\)  interactions,
where \( stands for vector bosons and \) f\( stands for fermions.Because nonzero spin assignments of the  boson have been excluded~\cite {Khachatryan:2014kca,Aad:2015mxa},we focus on the analysis of couplings of a spin-0  boson.Previous studies of anomalous \)\( couplings were performed by both the CMS and ATLASexperiments using either decay-onlyinformation~\cite {Chatrchyan:2012jja,Chatrchyan:2013mxa,Khachatryan:2014kca,Aad:2013xqa,Aad:2015mxa,Aaboud:2017oem},including associated productioninformation~\cite {Khachatryan:2016tnr,Sirunyan:2017tqd,Sirunyan:2019twz,Aad:2016nal,Aaboud:2017vzb,Aaboud:2018xdt},or including off-shell  boson production~\cite {Khachatryan:2015mma, Sirunyan:2019twz}.In this paper, we report a study of \)\( couplings using information from production of the  boson decaying to \)\( leptons.These results are combined with the previous CMS measurements using bothassociated production and decay information in the \) 4\( channel~\cite {Sirunyan:2019twz},resulting in stringent constraints on anomalous  boson couplings. Here and in the following\)\( denotes an electron or muon.\) The \(\rightarrow \)  decay has been observed by the
CMS experiment, with over five standard deviation significance [24]}.
The \(\rightarrow \)  sample can be used to study the quantum numbers of the \(\)  boson and its anomalous couplings
to SM particles, including its \(CP\)  properties.
The dominant production mechanisms of the \(\)  boson considered in this paper are shown at leading order
in QCD in Fig. REF . Anomalous \(\) , \(\) , \(\gamma \) , \(\gamma \gamma \) , and \(\)  couplings affect the correlations between the \(\)  boson, the beam line, and the two jets in vector boson fusion (VBF), in associated production with a vector boson decaying hadronically (\(\) , where \(, \) ), and also in gluon fusion production with additional two jets. The gluon fusion production with two additional jets appears at higher
order in QCD with an example of gluons appearing in place of the vector bosons shown in the VBF diagram in the middle of Fig. REF .
A study of anomalous \(\)  couplings in associated production with top quarks, \(\)  or \(\) ,
and anomalous \(\)  couplings in the decay of the \(\)  boson are also possible using \(\)  events [25]}.
However, more data are needed to reach sensitivity to such anomalous effects,
and it has been confirmed that these anomalous couplings would not affect the measurements presented in this paper.
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